This disclosure relates generally to the field of wellbore trajectory planning for multiple wells proximate each other drilled through subsurface formations. More specifically, the disclosure relates to techniques for more efficiently identifying well trajectories which do not present material risk of collision with other proximate wellbores.
Subsurface formations in a particular geographic area may have a one or more reservoirs containing economically useful materials such as oil and gas. In order to economically extract such materials wellbores may be drilled from selected positions on the Earth's surface or the bottom of a body of water such as a lake or ocean. Such wellbores may be drilled along preselected trajectories in order to reduce and/or minimize distances between surface or water bottom locations of the wellbores while intersecting one or more reservoirs or portions thereof by wellbores. Drilling along such preselected trajectories is known in the art as directional drilling. Directional drilling uses certain types of drilling tools, for example steerable drilling motors or rotary steerable directional drilling systems to cause a drill bit to drill the well along the preselected trajectory. It is also known in the art to measure the position of each well along its trajectory at selected positions in order to determine how closely the well is following the predetermined trajectory.
The measurements of position have inherent error because of limitations in the accuracy of the sensors used to make the measurements. Thus, the absolute position of any wellbore at any position along its trajectory is subject to a degree of uncertainty. A description of a standard technique for calculating positional uncertainty at any point along a particular wellbore is described in H. S. Williamson, Accuracy Prediction for Directional Measurement While Drilling, paper no. 67616, 15 (4), Society of Petroleum Engineers, Richardson, Tex. (December 2000). The positional uncertainty calculation according to methods such as described in the foregoing publication is computationally expensive and may be time consuming, including, in particular, the computation of separation distances between wells in detail over entire well trajectories.